Problem: Solve for $x$ and $y$ using substitution. ${-x-5y = 1}$ ${y = 2x-9}$
Answer: Since $y$ has already been solved for, substitute $2x-9$ for $y$ in the first equation. ${-x - 5}{(2x-9)}{= 1}$ Simplify and solve for $x$ $-x-10x + 45 = 1$ $-11x+45 = 1$ $-11x+45{-45} = 1{-45}$ $-11x = -44$ $\dfrac{-11x}{{-11}} = \dfrac{-44}{{-11}}$ ${x = 4}$ Now that you know ${x = 4}$ , plug it back into $\thinspace {y = 2x-9}\thinspace$ to find $y$ ${y = 2}{(4)}{ - 9}$ $y = 8 - 9$ $y = -1$ You can also plug ${x = 4}$ into $\thinspace {-x-5y = 1}\thinspace$ and get the same answer for $y$ : ${-}{(4)}{ - 5y = 1}$ ${y = -1}$